How do I convert an stl to an mdd file so that I can use the mesh cache modifier?
To convert stl files to mdd files import the stl, then export it to mdd using the official addon "NewTek MDD format" (just enable it).

Then you can use the mesh cache modifier, hopefully.

Another way could be, as I guess all stl files have the same vertices and similar structure, import all stl files as separate objects then select all them, and "join them as shape key". 

This will give the last selected object as "base" shape, and each other object as an animatable shape key...

I'm not sure about the general layout of your objects, and thus if this could work, since you described nothing about them, apart the file format and the intended usage...